Show that it applies to Mean Value Theorem: 0<y<x ; (x-y)/2<lnx/y<(x-y)/y

[Sabina]

Show that it applies to Mean Value Theorem: 0<y<x ; (x-y)/2<lnx/y<(x-y)/y

 

[Deleted member 4993]

Show that it applies to Mean Value Theorem: 0<y<x ; (x-y)/2<lnx/y<(x-y)/y

Do you know the MVT? If not - look into your class-notes or textbook or internet - and come back to tell us.

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

 

[Ishuda]

Show that it applies to Mean Value Theorem: 0<y<x ; (x-y)/2<lnx/y<(x-y)/y

What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

HINT: I would start at

For the ln(x/y)<(x-y)/y=(x/y)-1 part consider the function
f(t) = [1-t+ln(t)]; \(\displaystyle 0 \lt\ t \le \infty\)

For the (x-y)/2<ln(x/y) part consider the function
g(t) = t - ln(t); \(\displaystyle 0 \lt\ t \le \infty\)

 

[stapel]

Show that it applies to Mean Value Theorem: 0<y<x ; (x-y)/2<lnx/y<(x-y)/y

Is the second three-part inequality as follows?

. . . . .\(\displaystyle \dfrac{x\, -\, y}{2}\, <\, \dfrac{\ln(x)}{y}\, <\, \dfrac{x\, -\, y}{y}\)

What is the "it" that you need to "show" applying "to" the Mean Value Theorem? Or are you maybe actually supposed to be applying the Mean Value Theorem to the "sides" of this inequality, in order perhaps to prove the inequality to be true?

Please reply with the complete instructions, along with a clear listing of your thoughts and efforts so far, so we can see where things are bogging down. Thank you!